CHANCE, an accident or event, a phenomenon which has no apparent or discoverable cause; hence an event which has not been expected, a piece of good or bad fortune. From the popular idea that anything of which no assignable cause is known has therefore no cause, chance was regarded as having a substantial objective existence, being itself the source of such uncaused phenomena. For the philosophic theories relating to this subject see ACCIDENTALISM.
"Chance," in the theory of probability, is used in two ways. In the stricter or mathematical usage, it is synonymous with probability, i.e., if a particular event may occur in n ways in an aggregate of p events, then the "chance" of the particular event occurring is given by the fraction n/p. In the second usage, the at Weissenburg and in the Palatinate won the warm commenda tion of Hoche. He commanded the left wing of the French armies on the Rhine, between Neuwied and Dusseldorf, and took part in the expeditions to the Lahn and the Main. In 1798 Championnet was named commander-in-chief of the "army of Rome," which was protecting the infant Roman republic against the Neapolitan court and the British fleet. The Austrian general Mack had a tenfold superiority in numbers, but Championnet captured Naples itself and there set up the Parthenopean repub lic. But his intense earnestness and intolerance of opposition soon embroiled him with the civilians, and the general was recalled in disgrace. The following year, however, saw him again in the field as commander-in-chief of the "army of the Alps." The campaign which followed was uniformly unsuccessful, and, worn out by the unequal struggle, Championnet died at Antibes, on Jan. 9, 1800.
See A.R.C. de St. Albin, Championnet, ou les Campagnes de Hot lande, de Rome et de Naples (186o) ; M. Faure, Souvenirs du General Championnet (19o4)•